House Ways and Means Chairman Paul Ryan said Wednesday that Democrats opposed to President Barack Obama's free-trade push are finding out how difficult compromise with the White House can be. "There's a lot of irony in this story," he said.

"They're getting the taste of the same medicine that we've been getting for many years," the Wisconsin Republican told CNBC's "Squawk Box." He said it's not necessarily satisfying, but "it's clarifying."

Senate Democrats dug in Tuesday, blocking debate on a bill to renew the president's "fast track" authority to negotiate trade deals that can pass Congress without being amended.

Obama wants the power to negotiate the long-sought Trans-Pacific Partnership—an issue that's actually putting the White House and Republicans on the same side.

"I can't imagine the Democrats are going to deal the leader of the party, the president, this kind of defeat," Ryan said. "And I think we'll get through this."

The office of the U.S. Trade Representative describes the deal as an "agreement that will open markets, set high-standard trade rules ... and promote jobs and growth in the United States and across the Asia-Pacific region."

"So much is at stake," Ryan said.

"The global economy is happening. There's constant change," he continued. "Are we going to write the rules of the global economy or are we just going to cede it countries link China?"

Labor unions and liberals, including Sen. Elizabeth Warren from Massachusetts, oppose the deal—saying it would result in American job losses by making it easier for companies to outsource work and keep wages down.

"We're ready to go," said Ryan. "We, Republicans, believe in trade. And we believe in writing the rule book."

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